Standard

Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions. / Vostokov, S. V.; Haustov, N. V.; Zhukov, I. B.; Ivanova, O. Yu; Afanas’eva, S. S.

In: Vestnik St. Petersburg University: Mathematics, Vol. 51, No. 2, 01.04.2018, p. 114-123.

Research output: Contribution to journal › Article › peer-review

Harvard

Vostokov, SV, Haustov, NV, Zhukov, IB, Ivanova, OY & Afanas’eva, SS 2018, 'Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions', Vestnik St. Petersburg University: Mathematics, vol. 51, no. 2, pp. 114-123. https://doi.org/10.3103/S1063454118020103

APA

Vostokov, S. V., Haustov, N. V., Zhukov, I. B., Ivanova, O. Y., & Afanas’eva, S. S. (2018). Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions. Vestnik St. Petersburg University: Mathematics, 51(2), 114-123. https://doi.org/10.3103/S1063454118020103

Vancouver

Vostokov SV, Haustov NV, Zhukov IB, Ivanova OY, Afanas’eva SS. Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions. Vestnik St. Petersburg University: Mathematics. 2018 Apr 1;51(2):114-123. https://doi.org/10.3103/S1063454118020103

Author

Vostokov, S. V. ; Haustov, N. V. ; Zhukov, I. B. ; Ivanova, O. Yu ; Afanas’eva, S. S. / Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions. In: Vestnik St. Petersburg University: Mathematics. 2018 ; Vol. 51, No. 2. pp. 114-123.

BibTeX

@article{80c80d46d9664824ac384afc0d79a3ec,
title = "Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions",
abstract = "Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.",
keywords = "Hyodo inequality, ramification depth",
author = "Vostokov, {S. V.} and Haustov, {N. V.} and Zhukov, {I. B.} and Ivanova, {O. Yu} and Afanas{\textquoteright}eva, {S. S.}",
year = "2018",
month = apr,
day = "1",
doi = "10.3103/S1063454118020103",
language = "English",
volume = "51",
pages = "114--123",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Analogue of the Hyodo Inequality for the Ramification Depth in Degree p 2 Extensions

AU - Vostokov, S. V.

AU - Haustov, N. V.

AU - Zhukov, I. B.

AU - Ivanova, O. Yu

AU - Afanas’eva, S. S.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.

AB - Ramification in complete discrete valuation fields is studied. For the case of a perfect residue field, there is a well-developed theory of ramification groups. Hyodo introduced the concept of ramification depth associated with the different of an extension and obtained an inequality that combines the concept of ramification depth in a degree p2 cyclotomic extension with the concept of ramification depth in a degree p subextension. The paper gives a detailed consideration of the structure of degree p2 extensions that can be obtained by a composite of two degree p extensions. In this case, it is not required that the residue field be perfect. Using the concepts of wild and ferocious extensions and the defect of the main unit, degree p2 extensions are classified and more accurate estimates for the ramification depth are obtained. In a number of cases, exact formulas for ramification depth are presented.

KW - Hyodo inequality

KW - ramification depth

UR - http://www.scopus.com/inward/record.url?scp=85048654237&partnerID=8YFLogxK

U2 - 10.3103/S1063454118020103

DO - 10.3103/S1063454118020103

M3 - Article

AN - SCOPUS:85048654237

VL - 51

SP - 114

EP - 123

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -

ID: 36612936